First slide

Functions (XII)

Question

The range of the $y = \sqrt{x^{2} - 4}$ is

Easy

A

$(0, \infty)$
B

$[0, \infty)$
C

$(- \infty, - 2] \cup [2, \infty)$
D

None of these

Solution

$(i) \sqrt{x^{2} - 4}$
$Least value of square root is 0 when x^{2} = 4 or x = \pm 2 .$
$\begin{array}{l} Also, x^{2} - 4 \geq 0 \\ Hence, \sqrt{x^{2} - 4} \in [0, \infty) \end{array}$

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